It depends. Different tests for different complications. Heart disease - stress test, heart cath. For poor circulation & stroke - ultrasounds of blood vessels. For eyes, an exam of the retinas after dilating drops put in to widen the pupils. For kidneys, blood tests for bun, creatinine, and urine checks for protein. For nerve damage, checks for sensation to light touch & vibration.
Different tests. Diabetic patient are at greater risk for complications such as cardiovascular disease (high blood pressure, poor circulation), nerve damage (neuropathy), kidney damage (nephropathy), and eye damage (retinopathy). There are different test for different complications. Have your self evaluated to get the appropriate tests.